We experimentally realized an optical nanofiber-based cavity by combining a 1-D photonic crystal and Bragg grating structures. The cavity morphology comprises a periodic, triplex air-cube introduced at the waist of the nanofiber. The cavity has been theoretically characterized using FDTD simulations to obtain the reflection and transmission spectra. We have also experimentally measured the transmission spectra and a Q-factor of ~784(87) for a very short periodic structure has been observed. The structure provides strong confinement of the cavity field and its potential for optical network integration makes it an ideal candidate for use in nanophotonic and quantum information systems.